Got the S&W Historical Foundation letter today. (Thanks Mr. Jinks for the historical search and thanks murphydog for pointing me in that direction.)
The revolver is a .38 Double Action Fourth Model shipped from the factory on 4/17/1908 and delivered to the husband of the woman my grandfather bought the pistol from.
Also, I took it with me to the firing range last week. All I had at the time were the 5 rounds that had been in the gun for that last 30 years or so. But, they all fired fine. Hardly any recoil from this gun compared to my 2 S&W M&P 9mm's (the only other pistols I've fired).
I fired the first 3 rounds and all were high and left. Could be the shooter or it may be the sights/gun. So, I had my ex-US Marshall friend with over 40 years law enforcement experience fire the last 2 rounds. His shots were high and left also (which made me feel better about my shooting).
I've since ordered/received some more 38 ammo. So, I'll try again soon to see if I can figure out the aiming on this thing.
The sights are definitely much harder to see than the modern guns.

But, it's cool to have the historical letter now and to know for sure just how old the revolver is.

Thanks to all of you for your earlier comments and cleaning/storing suggestions.

Scott